Are you talking band saw or blade. Why not use a dedicated engine like a 20 HP Honda or Kohler. You could walk it down the track or power it down the track with hyd motor.
I can see where HP loss and heat could be an issue. I am building a band saw. The nice thing about hydraulics is it would be simple to shut off the band at the end of each run. A PTO drive would require some kind of clutch system, as would a dedicated engine. I want to avoid the expense and maintenance of another engine while I have a tractor.
PTO pump= 37 hp at the PTO so more hydraulic flow potential. Parts = PTO pump, band motor, priority cirucuit, drive motor, hoses, log turning hydraulic piston, control levers. A pro would be hydraulic controls, and fairly easy to detach to move more logs around with the tractor.
Tractor hydraulic pump = Less flow, possibly too little (8.6 gpm and 2500 psi at rated RPM). Parts = band motor, priority cirucuit, drive motor, hoses, log turning hydraulic piston, control levers. This is one $500 part less than the obove scenario. Also would be easy to disconnect. Does the tractor have any priority circuit? For example, I could run the band off the power beyond (backhoe) hydraulics and the other controls off of the 3rd SCV valve. Would this cause a pressure/flow drop in the primary system?
PTO direct = 37 HP available with more power transfer (overkill, but I would like to run at lower RPMs anyway for fuel and noise) This means a stationary cutter head which seems less ideal. Parts would be a gearbox and some kind of clutch system. I would still need hydraulic lines, a drive motor, controls and a piston. This is the gearbox and more sophisticated carriage versus the cost of a PTO pump and drive motor with priority control of the first option. I'm not sure what would cost more.
Dedicated engine = like everybody else does it. Expense is engine, clutch, fuel tank + mounting. It would be a lot noisier. I still need the hydraulic components for a log turning piston and carriage drive motor.